07-Str-B2 · December 2018

Question 3 of 6: Project Control — expense and payment S-curves, financing interest and overdraft limit

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format: National Exams, December 2018 — 07-Str-B2 Management of Construction. Three hours, closed book, one approved Casio or Sharp calculator permitted. Six questions of equal value (20 marks each); any five constitute a complete paper and only the first five that appear in the answer book are marked. All six are worked below so the paper serves as a complete revision set whichever five a candidate elects.

Reference texts: Hegazy, T., Computer-Based Construction Project Management (Prentice Hall) — activity-on-arrow and activity-on-node networks, forward and backward passes, total and free float, and the contractor cash-flow / overdraft model with mark-up, retention and payment lag; these chapters carry Questions 1 and 3. Hendrickson, C. & Au, T., Project Management for Construction (2nd ed., Carnegie Mellon) — Chapter 5 (cost estimation and unit-cost data), Chapter 8 (construction contracts and the allocation of risk), Chapter 10 (fundamental scheduling procedures) and Chapter 12 (cost control, monitoring and accounting, including project financing). Halpin, D.W. & Senior, B.A., Construction Management (4th ed., Wiley) — delivery systems, crew productivity and quantity take-off, surety bonding and lien law. R.S. Means, Building Construction Cost Data (annual) — the anatomy of a unit-price line (crew, daily output, labour-hours per unit, bare material / labour / equipment / total, and total including overhead and profit) and of the related crew table, behind Question 6. Sullivan, W.G., Wicks, E.M. & Koelling, C.P., Engineering Economy (17th ed., Pearson) — Chapters 4 and 5, the uniform-series present-worth factor and deferred annuities, used in Question 4. Canadian Construction Documents Committee, CCDC 2 Stipulated Price Contract (2020), CCDC 4 Unit Price Contract, CCDC 3 Cost Plus Contract, CCDC 14 Design-Build Stipulated Price Contract, and CCDC 220 Bid Bond, CCDC 221 Performance Bond and CCDC 222 Labour and Material Payment Bond — the Canadian contract and surety machinery behind Questions 2 and 5. Provincial lien statutes — the British Columbia Builders Lien Act (SBC 1997 c.45) and the Ontario Construction Act (RSO 1990 c.C.30, as amended 2018) — supply the Canadian equivalent of the American “mechanics lien” named in Question 5.

Check — how the two printed figures on page 2 were read. Network (Question 1): nine numbered event circles and eleven arrows, every arrow carrying a letter and a duration — A(4) 1→2, B(6) 1→4, C(2) 1→7, D(8) 2→3, E(4) 3→6, F(10) 4→5, G(16) 4→8, H(8) 5→6, I(6) 6→9, J(6) 7→8, K(10) 8→9. There is no dummy arrow on this drawing, so the translation to activity-on-node in part (c) is exact and needs no extra logic. Budget S-curve (Question 3): the six labelled markers fall squarely on months 1 to 6 of the printed axis (ticks 0 to 7). The project therefore runs six months and the budget (cost) at completion is $127,000.

Question 3: Project Control — expense and payment S-curves, financing interest and overdraft limit (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A six-month project whose budget (cost) S-curve, mark-up, retention, payment lag and financing rate are as tabulated:

Given data read from the paper
Month	1	2	3	4	5	6
Cumulative cost ($)	29,000	40,000	54,000	86,000	112,000	127,000
Cost in the month ($)	29,000	11,000	14,000	32,000	26,000	15,000
Mark-up 10 per cent · owner retention 5 per cent, released with the last payment · owner payment delay 1 month · interest 12 per cent per annum

Find. The cumulative expense curve plotted against the cumulative owner-payment curve, the total interest chargeable on the money the contractor must borrow, and the overdraft limit that has to be arranged.

Approach. Convert the budget curve into three parallel cumulative series — cash out (cost), value of work certified (cost plus mark-up, less retention) and cash in (that certified amount received one month later) — then roll a month-by-month bank balance forward, charging interest on the opening balance each month; the largest balance is the overdraft limit and the sum of the monthly interest is the financing cost.

Convert the budget curve into monthly expenses. The printed curve is cumulative, so the cash going out in month $t$ is the first difference: $$E_t=C_t-C_{t-1}$$ giving 29,000, 11,000, 14,000, 32,000, 26,000 and 15,000 dollars for months 1 to 6, which sum back to the $127,000 budget as a check.
Value the work and apply the mark-up. The contractor bills the owner for the work at cost plus mark-up, so the cumulative value of work done is $$V_t=(1+m)\,C_t=1.10\,C_t$$ At completion $V_6=1.10\times127{,}000=139{,}700$ dollars, so the contract value is $139,700 and the gross mark-up recovered over the job is $139{,}700-127{,}000=12{,}700$ dollars. That $12,700 is the pool out of which the financing cost calculated below must be paid.
Deduct retention to get the amount certified for payment. The owner withholds 5 per cent of every progress claim and releases the accumulated holdback with the final payment, so the cumulative amount certified during the job is $$P^{cum}_t=(1-r)\,V_t=0.95\times1.10\,C_t=1.045\,C_t$$ which gives 30,305, 41,800, 56,430, 89,870, 117,040 and 132,715 dollars at months 1 to 6. The retention held back is $$R=0.05\times139{,}700=6{,}985\ \text{dollars}$$ Differencing the cumulative certified amounts gives the individual certificates — 30,305, 11,495, 14,630, 33,440, 27,170 and 15,675 dollars — and the last one is augmented by the released retention to $15{,}675+6{,}985=22{,}660$ dollars. The six payments then sum to $139,700, the full contract value, which is the arithmetic check on the whole payment schedule.
(a) Apply the one-month payment lag and draw the two S-curves. A certificate issued at the end of month $t$ is honoured at the end of month $t+1$, so the contractor receives nothing in month 1, receives the month-1 certificate in month 2, and so on, with the final payment including the retention arriving in month 7 — one month after the work finishes. Plotting the cumulative cash received against the cumulative cash paid out gives the two curves in Figure 3.1; the vertical gap between them at any date is the money the contractor has tied up in the project, and it is that gap the bank has to fund.
Roll the bank balance forward with interest. With a nominal 12 per cent per annum charged monthly, the periodic rate is $$i=\frac{0.12}{12}=0.01\ \text{per month}$$ and the overdraft $N_t$ at the end of each month follows from $$N_t=N_{t-1}(1+i)+E_t-P_t$$ where $P_t$ is the cash actually received in month $t$. Working month by month: $N_1=0+29{,}000-0=29{,}000$; $N_2=29{,}000(1.01)+11{,}000-30{,}305=9{,}985$; $N_3=9{,}985(1.01)+14{,}000-11{,}495=12{,}589.85$; $N_4=12{,}589.85(1.01)+32{,}000-14{,}630=30{,}085.75$; $N_5=30{,}085.75(1.01)+26{,}000-33{,}440=22{,}946.61$; $N_6=22{,}946.61(1.01)+15{,}000-27{,}170=11{,}006.08$; and finally $N_7=11{,}006.08(1.01)+0-22{,}660=-11{,}543.86$, a credit balance.
(b) Read the two required answers off the table. The interest charged in each month is one per cent of that month's opening balance — nil, 290.00, 99.85, 125.90, 300.86, 229.47 and 110.06 dollars — so the financing cost of the job is $$\boxed{\sum I_t = 1{,}156.14\ \text{dollars of interest}}$$ and the deepest the account goes is at the end of month 4: $$\boxed{\text{Overdraft limit required}\approx30{,}100\ \text{dollars}\ (N_4=30{,}085.75)}$$ In practice the contractor would arrange a facility with a round-figure margin above this — say $35,000 — because the calculated peak carries no allowance for overruns or late payment: the peak sits about $7,100 above the month-5 balance, but if the month-4 certificate due in month 5 arrived a month late the month-5 balance would jump to about $56,400.
Check the closure. The account finishes in credit by $11,543.86, and that figure must equal total receipts less total expenses less total interest: $$139{,}700-127{,}000-1{,}156.14=11{,}543.86\ \checkmark$$ Financing has therefore consumed $1{,}156.14/12{,}700=9.1$ per cent of the gross mark-up, leaving the contractor a net profit of $11,543.86 on a $127,000 cost — about 9.1 per cent of cost rather than the 10 per cent the mark-up suggested.

Figure 3.1 — the cumulative expense (budget) S-curve plotted against the cumulative owner payments actually received, with the value of work including mark-up shown dashed for reference. The vertical gap between the red and blue curves is the contractor's cash exposure; it is widest at month 4, which is where the overdraft peaks.

Question 3 — month-by-month cash flow and overdraft (all figures in dollars)
Month	Opening balance	Interest at 1%	Cash out (cost)	Cash in (payment)	Closing balance
1	0.00	0.00	29,000	0	29,000.00
2	29,000.00	290.00	11,000	30,305	9,985.00
3	9,985.00	99.85	14,000	11,495	12,589.85
4	12,589.85	125.90	32,000	14,630	30,085.75
5	30,085.75	300.86	26,000	33,440	22,946.61
6	22,946.61	229.47	15,000	27,170	11,006.08
7	11,006.08	110.06	0	22,660	−11,543.86 (credit)
Contract value 139,700 · total cost 127,000 · total interest 1,156.14 · peak overdraft 30,085.75 at end of month 4 · net profit after financing 11,543.86

Topic. Contractor cash-flow forecasting from a budget S-curve: mark-up, retention, payment lag, overdraft and financing cost.

Key relations. Monthly cost $E_t=C_t-C_{t-1}$; value of work $V_t=(1+m)C_t$; amount certified $P^{cum}_t=(1-r)V_t$ with retention $R=rV_n$ released at the end; cash received in month $t$ equals the certificate of month $t-d$ for a lag of $d$ months; overdraft recursion $N_t=N_{t-1}(1+i)+E_t-P_t$ with $i=i_{nominal}/12$; and the closure identity $\sum P-\sum E-\sum I=-N_n$.

Why this works. Three separate delays each push cash out ahead of cash in, and the S-curve model simply stacks them. The contractor pays labour and suppliers as the work proceeds, but bills only at the end of the month; the owner then withholds a retention percentage; and the certified balance is not paid for a further month. The cumulative effect is that the contractor is always financing roughly one to two months of production plus the accumulated holdback, which is why the gap between the two curves in Figure 3.1 tracks the steepest part of the S-curve rather than its end. Charging interest on the opening balance is the conventional treatment because the bank's month starts with whatever was owed at the close of the previous one; the closure identity then provides a complete arithmetic check, since every dollar received must end up as either a dollar of cost, a dollar of interest, or a dollar of the closing balance.

Common pitfall. The most frequent error is applying the mark-up to the payments but forgetting that the retention is taken on the marked-up value, not on the cost — here $0.05\times139{,}700=6{,}985$, not $0.05\times127{,}000=6{,}350$. The second is to lose the seventh month: the final payment, retention included, arrives one month after the work is finished, and a table that stops at month 6 both under-states the interest and hides the fact that the account is still $11,006 in overdraft when the last worker leaves site. The third is to read the peak overdraft off the largest monthly expense rather than off the balance column — month 4 has the largest outlay here and does happen to carry the peak, but that coincidence does not hold in general.

Source. Hegazy, Computer-Based Construction Project Management, chapter on project cash flow and financing (the cost, revenue and overdraft profile); Hendrickson & Au, Project Management for Construction, Chapter 12, sections on financing of constructed facilities and cash-flow analysis.

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